Simplify the following expression: $ x = \dfrac{-9}{r + 4} + \dfrac{3}{4} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{-9}{r + 4} \times \dfrac{4}{4} = \dfrac{-36}{4r + 16} $ Multiply the second expression by $\dfrac{r + 4}{r + 4}$ $ \dfrac{3}{4} \times \dfrac{r + 4}{r + 4} = \dfrac{3r + 12}{4r + 16} $ Therefore $ x = \dfrac{-36}{4r + 16} + \dfrac{3r + 12}{4r + 16} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{-36 + 3r + 12}{4r + 16} $ $x = \dfrac{3r - 24}{4r + 16}$